{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import re\n",
    "import math\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "DAY = \"20200728\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>t</th>\n",
       "      <th>sym</th>\n",
       "      <th>px</th>\n",
       "      <th>qty</th>\n",
       "      <th>b5sz</th>\n",
       "      <th>b4sz</th>\n",
       "      <th>b3sz</th>\n",
       "      <th>b2sz</th>\n",
       "      <th>b1sz</th>\n",
       "      <th>b5px</th>\n",
       "      <th>...</th>\n",
       "      <th>a1px</th>\n",
       "      <th>a2px</th>\n",
       "      <th>a3px</th>\n",
       "      <th>a4px</th>\n",
       "      <th>a5px</th>\n",
       "      <th>a1sz</th>\n",
       "      <th>a2sz</th>\n",
       "      <th>a3sz</th>\n",
       "      <th>a4sz</th>\n",
       "      <th>a5sz</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2020-07-28D09:00:00.225798000</td>\n",
       "      <td>2330</td>\n",
       "      <td>4640000</td>\n",
       "      <td>13911</td>\n",
       "      <td>315</td>\n",
       "      <td>95</td>\n",
       "      <td>482</td>\n",
       "      <td>132</td>\n",
       "      <td>621</td>\n",
       "      <td>4620000</td>\n",
       "      <td>...</td>\n",
       "      <td>4645000</td>\n",
       "      <td>4650000</td>\n",
       "      <td>4655000</td>\n",
       "      <td>4660000</td>\n",
       "      <td>4665000</td>\n",
       "      <td>1831</td>\n",
       "      <td>1264</td>\n",
       "      <td>548</td>\n",
       "      <td>4108</td>\n",
       "      <td>10290</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2020-07-28D09:00:00.247359000</td>\n",
       "      <td>2330</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>315</td>\n",
       "      <td>95</td>\n",
       "      <td>482</td>\n",
       "      <td>132</td>\n",
       "      <td>621</td>\n",
       "      <td>4620000</td>\n",
       "      <td>...</td>\n",
       "      <td>4645000</td>\n",
       "      <td>4650000</td>\n",
       "      <td>4655000</td>\n",
       "      <td>4660000</td>\n",
       "      <td>4665000</td>\n",
       "      <td>1831</td>\n",
       "      <td>1265</td>\n",
       "      <td>548</td>\n",
       "      <td>4108</td>\n",
       "      <td>10290</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2020-07-28D09:00:00.247595000</td>\n",
       "      <td>2330</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>315</td>\n",
       "      <td>95</td>\n",
       "      <td>482</td>\n",
       "      <td>132</td>\n",
       "      <td>621</td>\n",
       "      <td>4620000</td>\n",
       "      <td>...</td>\n",
       "      <td>4645000</td>\n",
       "      <td>4650000</td>\n",
       "      <td>4655000</td>\n",
       "      <td>4660000</td>\n",
       "      <td>4665000</td>\n",
       "      <td>1831</td>\n",
       "      <td>1265</td>\n",
       "      <td>548</td>\n",
       "      <td>4108</td>\n",
       "      <td>10105</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2020-07-28D09:00:00.337188000</td>\n",
       "      <td>2330</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>315</td>\n",
       "      <td>95</td>\n",
       "      <td>482</td>\n",
       "      <td>132</td>\n",
       "      <td>627</td>\n",
       "      <td>4620000</td>\n",
       "      <td>...</td>\n",
       "      <td>4645000</td>\n",
       "      <td>4650000</td>\n",
       "      <td>4655000</td>\n",
       "      <td>4660000</td>\n",
       "      <td>4665000</td>\n",
       "      <td>1831</td>\n",
       "      <td>1265</td>\n",
       "      <td>548</td>\n",
       "      <td>4108</td>\n",
       "      <td>10105</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2020-07-28D09:00:00.340030000</td>\n",
       "      <td>2330</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>315</td>\n",
       "      <td>95</td>\n",
       "      <td>482</td>\n",
       "      <td>132</td>\n",
       "      <td>630</td>\n",
       "      <td>4620000</td>\n",
       "      <td>...</td>\n",
       "      <td>4645000</td>\n",
       "      <td>4650000</td>\n",
       "      <td>4655000</td>\n",
       "      <td>4660000</td>\n",
       "      <td>4665000</td>\n",
       "      <td>1831</td>\n",
       "      <td>1265</td>\n",
       "      <td>548</td>\n",
       "      <td>4108</td>\n",
       "      <td>10105</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 24 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                               t   sym       px    qty  b5sz  b4sz  b3sz  \\\n",
       "0  2020-07-28D09:00:00.225798000  2330  4640000  13911   315    95   482   \n",
       "1  2020-07-28D09:00:00.247359000  2330        0      0   315    95   482   \n",
       "2  2020-07-28D09:00:00.247595000  2330        0      0   315    95   482   \n",
       "3  2020-07-28D09:00:00.337188000  2330        0      0   315    95   482   \n",
       "4  2020-07-28D09:00:00.340030000  2330        0      0   315    95   482   \n",
       "\n",
       "   b2sz  b1sz     b5px  ...     a1px     a2px     a3px     a4px     a5px  \\\n",
       "0   132   621  4620000  ...  4645000  4650000  4655000  4660000  4665000   \n",
       "1   132   621  4620000  ...  4645000  4650000  4655000  4660000  4665000   \n",
       "2   132   621  4620000  ...  4645000  4650000  4655000  4660000  4665000   \n",
       "3   132   627  4620000  ...  4645000  4650000  4655000  4660000  4665000   \n",
       "4   132   630  4620000  ...  4645000  4650000  4655000  4660000  4665000   \n",
       "\n",
       "   a1sz  a2sz  a3sz  a4sz   a5sz  \n",
       "0  1831  1264   548  4108  10290  \n",
       "1  1831  1265   548  4108  10290  \n",
       "2  1831  1265   548  4108  10105  \n",
       "3  1831  1265   548  4108  10105  \n",
       "4  1831  1265   548  4108  10105  \n",
       "\n",
       "[5 rows x 24 columns]"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "raw_df = pd.read_csv(f\"tick_2330/tick_2330_{DAY}.csv\")\n",
    "raw_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Calculate VOI\n",
    "def delta_vtb(rows):\n",
    "    row0 ,row1 = rows.iloc[0], rows.iloc[1]\n",
    "    if np.less(row1[\"b1px\"], row0[\"b1px\"]):\n",
    "        return 0\n",
    "    if np.equal(row1[\"b1px\"], row0[\"b1px\"]):\n",
    "        return np.subtract(row1[\"b1sz\"], row0[\"b1sz\"])\n",
    "    return row1[\"b1sz\"]\n",
    "\n",
    "def delta_vta(rows):\n",
    "    row0 ,row1 = rows.iloc[0], rows.iloc[1]\n",
    "    if np.less(row1[\"a1px\"], row0[\"a1px\"]):\n",
    "        return row1[\"a1sz\"]\n",
    "    if np.equal(row1[\"a1px\"], row0[\"a1px\"]):\n",
    "        return np.subtract(row1[\"a1sz\"], row0[\"a1sz\"])\n",
    "    return 0\n",
    "\n",
    "def chunker(seq):\n",
    "    return (seq.iloc[pos:pos + 2] for pos in range(0, len(seq)-1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "drop_ls = ['b5sz','b4sz','b3sz','b2sz','b5px','b4px','b3px','b2px','a2px','a3px','a4px','a5px','a2sz','a3sz','a4sz','a5sz']\n",
    "\n",
    "def Preprocessing(df):\n",
    "    filter_ = (df['sym'] == 2330)\n",
    "    df = df[filter_]\n",
    "    start = df['t'] >= f'{DAY[:4]}-{DAY[4:6]}-{DAY[6:]}D09:05:00.000000000'\n",
    "    end = df['t'] <= f'{DAY[:4]}-{DAY[4:6]}-{DAY[6:]}D13:25:00.000000000'\n",
    "    df = df[(start&end)]\n",
    "    df = df.drop(drop_ls, axis = 1)\n",
    "    return df\n",
    "\n",
    "df = Preprocessing(raw_df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
       "      <th>t</th>\n",
       "      <th>sym</th>\n",
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       "  <tbody>\n",
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       "      <th>11192</th>\n",
       "      <td>2020-07-28D09:05:00.006032000</td>\n",
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       "      <th>11193</th>\n",
       "      <td>2020-07-28D09:05:00.044259000</td>\n",
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       "      <th>11194</th>\n",
       "      <td>2020-07-28D09:05:00.056901000</td>\n",
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       "      <th>11195</th>\n",
       "      <td>2020-07-28D09:05:00.066693000</td>\n",
       "      <td>2330</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>462</td>\n",
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       "      <td>4660000</td>\n",
       "      <td>1368</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11196</th>\n",
       "      <td>2020-07-28D09:05:00.109818000</td>\n",
       "      <td>2330</td>\n",
       "      <td>4660000</td>\n",
       "      <td>2</td>\n",
       "      <td>462</td>\n",
       "      <td>4655000</td>\n",
       "      <td>4660000</td>\n",
       "      <td>1366</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                   t   sym       px  qty  b1sz     b1px  \\\n",
       "11192  2020-07-28D09:05:00.006032000  2330  4660000    2   461  4655000   \n",
       "11193  2020-07-28D09:05:00.044259000  2330  4660000    1   461  4655000   \n",
       "11194  2020-07-28D09:05:00.056901000  2330        0    0   462  4655000   \n",
       "11195  2020-07-28D09:05:00.066693000  2330        0    0   462  4655000   \n",
       "11196  2020-07-28D09:05:00.109818000  2330  4660000    2   462  4655000   \n",
       "\n",
       "          a1px  a1sz  \n",
       "11192  4660000  1369  \n",
       "11193  4660000  1368  \n",
       "11194  4660000  1368  \n",
       "11195  4660000  1368  \n",
       "11196  4660000  1366  "
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.7/site-packages/ipykernel_launcher.py:4: FutureWarning: set_value is deprecated and will be removed in a future release. Please use .at[] or .iat[] accessors instead\n",
      "  after removing the cwd from sys.path.\n",
      "/usr/local/lib/python3.7/site-packages/ipykernel_launcher.py:8: FutureWarning: set_value is deprecated and will be removed in a future release. Please use .at[] or .iat[] accessors instead\n",
      "  \n"
     ]
    }
   ],
   "source": [
    "current_px = current_qty = 0\n",
    "for index, row in df.iterrows():\n",
    "    if row[\"px\"] == 0:\n",
    "        df.set_value(index, 'px', current_px)\n",
    "    else:\n",
    "        current_px = row[\"px\"]\n",
    "    if row[\"qty\"] == 0:\n",
    "        df.set_value(index, 'qty', current_qty)\n",
    "    else:\n",
    "        current_qty = row[\"qty\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>t</th>\n",
       "      <th>sym</th>\n",
       "      <th>px</th>\n",
       "      <th>qty</th>\n",
       "      <th>b1sz</th>\n",
       "      <th>b1px</th>\n",
       "      <th>a1px</th>\n",
       "      <th>a1sz</th>\n",
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       "      <th>11192</th>\n",
       "      <td>2020-07-28D09:05:00.006032000</td>\n",
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       "      <th>11193</th>\n",
       "      <td>2020-07-28D09:05:00.044259000</td>\n",
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       "      <td>2020-07-28D09:05:00.056901000</td>\n",
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       "      <td>2020-07-28D09:05:00.066693000</td>\n",
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       "      <td>4660000</td>\n",
       "      <td>1368</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11196</th>\n",
       "      <td>2020-07-28D09:05:00.109818000</td>\n",
       "      <td>2330</td>\n",
       "      <td>4660000</td>\n",
       "      <td>2</td>\n",
       "      <td>462</td>\n",
       "      <td>4655000</td>\n",
       "      <td>4660000</td>\n",
       "      <td>1366</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                   t   sym       px  qty  b1sz     b1px  \\\n",
       "11192  2020-07-28D09:05:00.006032000  2330  4660000    2   461  4655000   \n",
       "11193  2020-07-28D09:05:00.044259000  2330  4660000    1   461  4655000   \n",
       "11194  2020-07-28D09:05:00.056901000  2330  4660000    1   462  4655000   \n",
       "11195  2020-07-28D09:05:00.066693000  2330  4660000    1   462  4655000   \n",
       "11196  2020-07-28D09:05:00.109818000  2330  4660000    2   462  4655000   \n",
       "\n",
       "          a1px  a1sz  \n",
       "11192  4660000  1369  \n",
       "11193  4660000  1368  \n",
       "11194  4660000  1368  \n",
       "11195  4660000  1368  \n",
       "11196  4660000  1366  "
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "VOI = list()\n",
    "\n",
    "for group in chunker(df):\n",
    "    VOI.append(delta_vtb(group) - delta_vta(group))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "143439"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(VOI)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Calculate LOG_RETURN\n",
    "def log_return(rows):\n",
    "    return np.log(rows.iloc[0][\"px\"]/rows.iloc[1][\"px\"])\n",
    "\n",
    "log_list = list()\n",
    "count = 0\n",
    "for group in chunker(df):\n",
    "    log_list.append(log_return(group))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "VOI_np = np.array(VOI)\n",
    "\n",
    "unique, counts = np.unique(VOI_np, return_counts=True)\n",
    "VOI_count = dict(zip(unique, counts))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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gyWiSJ5OMJ1k96Pno2LB/SBga0qGZPegJACSZBXwH+BiwA9iaZGNVPTHYmWlQDuaP+vDqO3n66x8/grOR3v6OlncG5wLjVfVUVb0O3AIsG/CcxJF7pT3VK/rh1Xce0mN27+e7A+ngpaoGPQeSXAaMVtVft+3PAOdV1dX7jVsFrGqb7weePMSHPBX47SHuO1O4Rr1xnabnGvWmH+v051U1NFnHUXGaqFdVtRZY+1aPk2SsqkYOw5Tetlyj3rhO03ONejPodTpaThPtBBZ2bS9oNUlSHxwtYbAVWJTk9CTHAVcAGwc8J0maMY6K00RVtTfJ1cAmYBawrqoeP4IP+ZZPNc0ArlFvXKfpuUa9Geg6HRUfIEuSButoOU0kSRogw0CSNPPCwJ+96EiyLsmuJI911U5JsjnJ9nY/t9WTZE1bs0eSnD24mfdPkoVJ7k3yRJLHk1zT6q5TlyQnJHkgyS/bOn251U9Pcn9bjx+1i0NIcnzbHm/9w4Ocfz8lmZXkoSR3tO2jZo1mVBh0/ezFxcBi4Mokiwc7q4G5GRjdr7Ya2FJVi4AtbRs667Wo3VYBN/ZpjoO2F/hiVS0GlgBXtf9eXKc/9hpwQVWdAZwJjCZZAnwDuKGq3gfsAVa28SuBPa1+Qxs3U1wDbOvaPnrWqKpmzA04H9jUtX0tcO2g5zXA9RgGHuvafhI4rbVPA55s7X8Erpxs3Ey6AbfT+f0s12nqNfoT4BfAeXS+TTu71f/wb4/OVYPnt/bsNi6Dnnsf1mYBnRcPFwB3ADma1mhGvTMA5gPPdm3vaDV1zKuq51r7eWBea8/4dWtv088C7sd1epN2+uNhYBewGfg18FJV7W1DutfiD+vU+l8G3tPfGQ/Et4AvAb9v2+/hKFqjmRYG6lF1XpJ43TGQ5N3Aj4EvVNUr3X2uU0dVvVFVZ9J59Xsu8IEBT+mokuQTwK6qenDQc5nKTAsDf/biwF5IchpAu9/V6jN23ZK8k04Q/KCqftLKrtMUquol4F46pzzmJNn3xdbutfjDOrX+k4EX+zzVfvsw8MkkT9P5VeYLgG9zFK3RTAsDf/biwDYCK1p7BZ1z5Pvqy9vVMkuAl7tOk7xtJQlwE7Ctqr7Z1eU6dUkylGROa59I53OVbXRC4bI2bP912rd+lwH3tHdYb1tVdW1VLaiqYTp/d+6pqk9zNK3RoD9UGcCHOJcA/0nnnObfD3o+A1yHHwLPAf9L51zlSjrnJLcA24F/A05pY0PnKqxfA48CI4Oef5/W6CN0TgE9Ajzcbpe4Tm9ap78AHmrr9BjwD63+XuABYBz4F+D4Vj+hbY+3/vcO+jn0eb0+CtxxtK2RP0chSZpxp4kkSZMwDCRJhoEkyTCQJGEYSJIwDCRJGAaSJOD/AMfUb209ZgesAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.bar(range(len(VOI_count)), list(VOI_count.values()), align='center')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "log_np = np.array(log_list)\n",
    "\n",
    "unique, counts = np.unique(log_np, return_counts=True)\n",
    "log_count = dict(zip(unique, counts))\n",
    "plt.bar(range(len(log_count)), list(log_count.values()), align='center')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.7/site-packages/numpy/core/fromnumeric.py:2542: FutureWarning: Method .ptp is deprecated and will be removed in a future version. Use numpy.ptp instead.\n",
      "  return ptp(axis=axis, out=out, **kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       0.000\n",
      "Model:                            OLS   Adj. R-squared:                  0.000\n",
      "Method:                 Least Squares   F-statistic:                     15.15\n",
      "Date:                Wed, 14 Oct 2020   Prob (F-statistic):           9.91e-05\n",
      "Time:                        15:26:13   Log-Likelihood:             9.2304e+05\n",
      "No. Observations:              143439   AIC:                        -1.846e+06\n",
      "Df Residuals:                  143437   BIC:                        -1.846e+06\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const       6.437e-07   1.03e-06      0.628      0.530   -1.37e-06    2.65e-06\n",
      "X          -9.323e-08   2.39e-08     -3.893      0.000    -1.4e-07   -4.63e-08\n",
      "==============================================================================\n",
      "Omnibus:                    29346.443   Durbin-Watson:                   2.243\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):          1116594.849\n",
      "Skew:                          -0.021   Prob(JB):                         0.00\n",
      "Kurtosis:                      16.668   Cond. No.                         42.8\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "#逐筆比較\n",
    "import statsmodels.api as sm\n",
    "series_dict={'X':VOI,'y':log_list}\n",
    "cal=pd.DataFrame(series_dict)\n",
    "X=cal[['X']]\n",
    "y=cal[['y']]\n",
    "x = sm.add_constant(X)\n",
    "ols_results = sm.OLS(y, x).fit()\n",
    "print(ols_results.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
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